In this paper, we address the problem of the statistical multiplexing of video streams. Dynamic bitrate allocation is used to improve the overall video quality of a pool of channels. The balance is obtained by providing more bits to complex channels, while deprivations are applied to non-complex ones. In this study, the error minimization optimization of several compressed video is considered along with different metrics in order to exhibit a repartition key for bitrate sharing among all the channels. The goal of this approach is to introduce a reactivity parameter able to manage the bit transfer between channels. The validity of the parametric model is verified on two particular values, and compared to a static repartition solution.